1. Field of the Invention
The present invention relates to exposure technique and, more specifically, to an improvement of exposure technique taking into consideration the influence of aberration.
2. Description of the Background Art
Recently, elements constituting a semiconductor device, which is formed of a plurality of layers, come to be smaller and smaller. Therefore, registration accuracy of the elements formed in various layers of the semiconductor device comes to be more important. In addition, as the element has been miniaturized, influence to exposure caused by aberration of the optical system becomes significant.
The aforementioned registration accuracy is related to the following factors of errors.
(i) registration error: registration error in general meaning; PA1 (ii) alignment error: errors in X, Y and .theta. directions in aligned chip; PA1 (iii) machine stability and compatibility error: error inherent to the aligner itself; PA1 (iv) mask error: error in pattern location from ideal point of each coordinate point of the mask; PA1 (v) mask thermal expansion error: registration error derived from thermal expansion of the mask in the aligner; PA1 (vi) residual error: error caused by bending when the mask or the wafer is fixed, non linear distortion at high temperature heat treatment of the wafer and so on. PA1 (i) bundle of rays emitted in point symmetry from an object point must form an image of point symmetry at the image point, PA1 (ii) an image of a two dimensional object should be two dimensional, and PA1 (iii) lateral magnification should be constant anywhere in the image.
Of the various factors of registration error mentioned above, here, (i) registration error will be described.
First, referring to the figures, registration error measurement mark for measuring the registration error will be described, taking an MOS transistor as an example.
FIG. 54 is a vertical section of a general MOS transistor, and FIG. 55 is a plane view of a semiconductor device including the MOS transistor.
Referring to these figures, the structure of the MOS transistor will be briefly described. First, on a semiconductor substrate 76, a word line 80A constituting a gate electrode is formed, with a gate oxide film 78 interposed. Source/drain regions 77 are formed in semiconductor substrate 76.
Above gate electrode 80A, a bit line 82A is formed, with an interlayer oxide film 80 interposed. Bit line 82A is electrically connected to one of source/drain region 77. Word line 80A and bit line 82A are arranged orthogonally crossing each other as shown in FIG. 55. An interlayer oxide film 83 is formed on bit line 82A.
Referring to FIG. 55, assume that in the semiconductor device having the above-described structure, a contact hole 74 is formed in an active region 85 between word lines 80A and bit lines 82A which word lines and bit lines are arranged apart by 1 .mu.m from each other. The line width of word line 80A and the line width of bit line 82A are both 0.4 .mu.m.
The size of the contact hole 74 opened in the semiconductor device is 0.5 .mu.m.times.0.5 .mu.m. Therefore, when word lines 80A and bit lines 82A and contact hole 74 are formed registered exactly as designed, the distance X in the X direction between word line 80A and contact hole 74 and the distance Y in Y direction between bit line 82A and contact hole 74 would be both 0.25 .mu.m.
However, contact hole 74 may be opened out of position because of registration error. In that case, it is possible that part of the contact hole 74 is opened in word line 80A or bit line 82A.
Here, contact hole 74 is opened by the following manner. First, as shown in FIG. 54, a resist film 84A formed on interlayer oxide film 83 is patterned by photolithography, and using the patterned resist film 84A, the contact hole is opened.
Therefore, after the resist film 84A is patterned, deviation between the position of the pattern for the contact hole formed in resist film 84A and the positions of word lines 80A and bit lines 82A is measured, and if the contact hole pattern of the resist film is not accurate, only the resist film 84A have to be formed again.
However, the space between the contact hole 74 and word line 80A or between contact hole 74 and bit line 82A is as small as 0.25 .mu.m, and therefore it is difficult to measure registration error in this region.
Therefore, a method has been proposed in which a registration error measurement mark as a dummy pattern for measuring registration error is formed in a peripheral region around a semiconductor forming region simultaneously with the formation of the resist film, the word line and the bit line, and by measuring registration error of the measurement mark, registration error between the contact hole pattern of the resist film and the word lines and bit lines is measured.
The registration error measurement mark will be described with reference to FIGS. 56 and 57. First, referring to FIG. 56, arrangement of the registration error measurement mark will be described. In a peripheral region of the semiconductor device, a first measurement mask 80B is formed at a prescribed position simultaneously with word line 80A on gate oxide film 78.
Planar shape of the first measurement mark 80B is a square of 25 .mu.m.times.25 .mu.m as shown in FIG. 24A. Further, a second measurement mark 82B is formed at a prescribed position of interlayer oxide film 80, simultaneously with bit line 82A. The planar shape of second measurement mark 82B is also a square of 25 .mu.m.times.25 .mu.m, similar to the first measurement mark 80B of FIG. 57.
Above the first measurement mark 80B and the second measurement mark 82B on interlayer insulating film 83, third and fourth measurement marks 84B and 84C are formed simultaneously with the patterning of the resist film.
The size of the third and fourth measurement marks 84B and 84C is 15 .mu.m.times.15 .mu.m as shown in FIG. 57(a).
The first to fourth measurement marks 80B, 82B, 84B and 84C are adapted to have square planar shape, in order to meet the requirement of a measurement inspecting apparatus (for example, KLA5011 manufactured by KLA), allowing recognition of the positions of the sides of the square. The length of one side of the mark is required to be 15 to 30 .mu.m for the first and second measurement marks and 7.5 to 15 .mu.m for the third and fourth measurement marks. By the present technique, it is impossible to inspect registration of smaller dimensions.
Referring to FIG. 57, measurement of registration error between the word line 80A and the contact hole pattern of the resist film using the first and the third measurement marks 80B and 84B will be described.
FIG. 57(a) is a plane view from above of the third measurement mark 84B. FIG. 57(b) is a cross section taken along the line LVII(a)--LVII(a) of FIG. 57(a). FIG. 57(c) shows brightness of detection signal corresponding to the cross section taken along the line LVII(a)--LVII(a) of FIG. 57(a).
As can be seen from the figure, at the positions of side walls 10a, 10b, 11a and 11b of the first and third measurement marks 80B and 84B, the detection signal becomes dark. Here, by using the detection signal, registration error between word line 80A and the contact hole pattern of the resist film is measured.
For example, the center between the detection signals corresponding to the side walls 10a and 10b is found and the center c.sub.2 of the detection signals corresponding to side walls 11a and 11b is found. When the positions of the centers c.sub.1 and c.sub.2 coincide with each other, the deviation between the first and third measurement marks 80B and 84B is zero. When the positions of centers c.sub.1 and c.sub.2 do not coincide with each other, the difference therebetween corresponds to the amount of deviation between the first and third measurement marks 80B and 84B. This amount of deviation is in one to one correspondence with the amount of deviation between word line 80A and the contact hole pattern of the resist film, and hence it can be directly regarded as registration error.
The amount of deviation between the second and fourth measurement marks 82B and 84C can also be found by the similar manner.
In the example of FIG. 57, both the first and third measurement marks 80B and 84B are positive pattern. However, even in the example of FIG. 58(a) in which both the first and third measurement marks 180B and 184B are negative patterns, the amount of deviation between the first and third measurement marks 180B and 184B can be found in the similar manner as the example of FIG. 57, by finding the center between detection signals corresponding to side walls 110a and 110b and the center between the detection signals corresponding to side walls 111a and 111b. In this case also, the amount of deviation can be regarded divided as the registration error.
However, the measurement of registration error described above undergoes the influence of aberration, so that the amount of deviation between the contact hole pattern and the word line or the bit line is not exactly in one to one correspondence to the amount of deviation between the measurement marks.
The aberration will be briefly described. An optical system should ideally satisfy the following conditions of image formation. Namely,
These requirements are for monochromic light. However, these should desirably be satisfied when polychromatic light (white light) is used. Deviation from the ideal conditions of image formation is referred to as aberration.
The aberration caused when the condition (i) is not satisfied is referred to as spherical aberration, a stigmatism or comatic aberration.
The aberration caused if the condition (ii) is not satisfied is referred to as aberration caused by the curvature of field.
The aberration caused if the condition (iii) is not satisfied is referred to as distortion aberration.
Here, the comatic aberration, which has the most significant influence in measuring the registration error will be described with reference to FIGS. 59 to 64.
First, referring to FIG. 59, comatic aberration caused at an opening in a photomask will be described. It is assumed that the photomask includes not only a general photomask but also a phase shift mask and an attenuation type phase shift mask.
FIG. 59(a) shows a cross sectional structure of a photo mask 110. On a transparent substrate 211, a light transmitting portion 212B and a light intercepting portion 212A (having the hole diameter of 0.4 .mu.m) are formed. Intensity of light 220 which has past through light transmitting portion 212B on resist film 4 should be as shown by the solid line 221 of FIG. 59(b). However, because of the influence of comatic aberration, the light intensity significantly deviates from the ideal curves in one direction only. Therefore the right hand portion exhibits such intensity as represented by the dotted line 222.
As a result, in resist film 4, a hole having not the intended size L.sub.1 but the size L.sub.2 (L.sub.2 &gt;L.sub.1) is opened as shown in FIG. 59(c).
Referring to FIG. 60, an example will be described in which light transmitting portion 232B formed on photomask 230 is larger than the photomask 210 of FIG. 59. FIG. 60(a) shows a cross sectional structure of photomask 230. On a transparent substrate 231, a light transmitting portion 232B and a light intercepting portion 232A (having the hole diameter of 3.0 .mu.m) are formed. Intensity of light 220 which has past through light transmitting portion 232B on resist film 4 should be as shown by the solid line 221 of FIG. 60(b).
However, as already described with reference to FIG. 26, light intensity significantly deviates from the ideal carve only in one direction because of the influence of comatic aberration. Therefore, the light intensity on the right hand portion is as shown by the dotted line 222.
As a result, in resist film 4, a hole not having the intended size L.sub.3 but having the size L.sub.4 is opened as shown in FIG. 60(c). It is also known that the larger the opening area of the light transmitting portion of the photomask, the larger the influence of comatic aberration.
Influence of comatic aberration on negative patterns have been described with reference to FIGS. 59 and 60. The influence of comatic aberration on positive patterns will be described with reference to FIG. 61.
FIG. 61(a) shows a cross sectional structure of a photomask 240. On a transparent substrate 241 of photomask 240, a prescribed positive pattern 242A is formed. The intensity of light 220 which has past through the photomask 240 should be as shown by the solid line 221 of FIG. 61(b) on resist film 4. However, because of the influence of comatic aberration, the light intensity is deviated only in one direction, and therefore on the left side portion, the light intensity becomes as shown by the dotted line 222.
As a result, in resist film 4, a pattern not having the intended size L.sub.5 but the size L.sub.6 is left as shown in FIG. 61(c). Therefore, as shown in FIGS. 59 to 61, both photomasks having positive patterns and negative patterns undergo the influence of comatic aberration.
The relation between the size of the pattern of the photo mask and the amount of deviation in light intensity caused by comatic aberration for a common photomask and for a phase shift mask are plotted in FIGS. 62 and 63.
As can be seen from these graphs, no matter whether it is a common photomask or a phase shift mask, the larger the pattern opening, the larger the influence of comatic aberration, and the larger the amount of deviation.
Accordingly, even when registration error is measured by using marks, the measured registration error is not in one to one correspondence with the error of the patterns constituting the semiconductor device, since the influence of comatic aberration on the marks differ from the influence on the patterns constituting the semiconductor device.
The comatic aberration influences not only the measurement of registration error but also the pattern exposure when the semiconductor device is formed. Let us consider an example, such as shown in FIG. 64(a), in which light transmitting portions 252A and 252B having different opening areas are formed on a transparent substrate 251 of one photomask 250.
Intensity of light which has past through light transmitting portion 252A on resist film 4 should be as shown by the solid line 221A and intensity of light which has past through light transmitting portion 252B should be as shown by the solid line 221B of FIG. 64(b). However, because of the influence of comatic aberration, on the right hand side, the intensity of light which has past through portion 252A is deviated as represented by the dotted line 222A, and the intensity of light which has past through the portion 252B is deviated to the right of the solid line 221B, as shown in the dotted line 222B.
The amount of deviation L.sub.9 of the dotted line 222A and the amount of deviation L.sub.12 of dotted line 222B are not equal to each other, and these amounts depend on the opening area of the light transmitting portion. Therefore, there are a plurality of different amounts of deviations defined by the size of the pattern. As a result, holes not having the intended size but including amount of deviation are opened in resist film 4, as shown in FIG. 64(c).